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3 pages, 189 KiB

Open AccessEditorial

Special Issue Editorial: “Discrete and Continuous Memristive Nonlinear Systems and Symmetry”

by Shaobo He

Symmetry 2023, 15(1), 167; https://doi.org/10.3390/sym15010167 - 6 Jan 2023

Viewed by 1188

Abstract

Memristor, as the fourth basic electronic component, was first reported by Chua in 1971 [...] Full article

(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)

Research

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14 pages, 1319 KiB

Open AccessArticle

A Ferroelectric Memristor-Based Transient Chaotic Neural Network for Solving Combinatorial Optimization Problems

by Zhuosheng Lin and Zhen Fan

Symmetry 2023, 15(1), 59; https://doi.org/10.3390/sym15010059 - 26 Dec 2022

Cited by 3 | Viewed by 1902

Abstract

A transient chaotic neural network (TCNN) is particularly useful for solving combinatorial optimization problems, and its hardware implementation based on memristors has attracted great attention recently. Although previously used filamentary memristors could provide the desired nonlinearity for implementing the annealing function of a [...] Read more.

A transient chaotic neural network (TCNN) is particularly useful for solving combinatorial optimization problems, and its hardware implementation based on memristors has attracted great attention recently. Although previously used filamentary memristors could provide the desired nonlinearity for implementing the annealing function of a TCNN, the controllability of filamentary switching still remains relatively poor, thus limiting the performance of a memristor-based TCNN. Here, we propose to use ferroelectric memristor to implement the annealing function of a TCNN. In the ferroelectric memristor, the conductance can be tuned by switching the lattice non-centrosymmetry-induced polarization, which is a nonlinear switching mechanism with high controllability. We first establish a ferroelectric memristor model based on a ferroelectric tunnel junction (FTJ), which exhibits the polarization-modulated tunnel conductance and the nucleation-limited-switching (NLS) behavior. Then, the conductance of the ferroelectric memristor is used as the self-feedback connection weight that can be dynamically adjusted. Based on this, a ferroelectric memristor-based transient chaotic neural network (FM-TCNN) is further constructed and applied to solve the traveling salesman problem (TSP). In 1000 runs for 10-city TSP, the FM-TCNN achieves a shorter average path distance, a 32.8% faster convergence speed, and a 2.44% higher global optimal rate than the TCNN. Full article

(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)

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9 pages, 1036 KiB

Open AccessArticle

Discrete Memristance and Nonlinear Term for Designing Memristive Maps

by Janarthanan Ramadoss, Othman Abdullah Almatroud, Shaher Momani, Viet-Thanh Pham and Vo Phu Thoai

Symmetry 2022, 14(10), 2110; https://doi.org/10.3390/sym14102110 - 11 Oct 2022

Cited by 13 | Viewed by 2087

Abstract

Chaotic maps have simple structures but can display complex behavior. In this paper, we apply discrete memristance and a nonlinear term in order to design new memristive maps. A general model for constructing memristive maps has been presented, in which a memristor is [...] Read more.

Chaotic maps have simple structures but can display complex behavior. In this paper, we apply discrete memristance and a nonlinear term in order to design new memristive maps. A general model for constructing memristive maps has been presented, in which a memristor is connected in serial with a nonlinear term. By using this general model, different memristive maps have been built. Such memristive maps process special fixed points (infinite and without fixed point). A typical memristive map has been studied as an example via fixed points, bifurcation diagram, symmetry, and coexisting iterative plots. Full article

(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)

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14 pages, 4596 KiB

Open AccessArticle

K-Means Clustering Algorithm Based on Memristive Chaotic System and Sparrow Search Algorithm

by Yilin Wan, Qi Xiong, Zhiwei Qiu and Yaohan Xie

Symmetry 2022, 14(10), 2029; https://doi.org/10.3390/sym14102029 - 28 Sep 2022

Cited by 6 | Viewed by 2241

Abstract

With the advent of the big data era, it is vital to explore the information involved in this type of data. With the continuous development of higher education, the K-means clustering algorithm is widely used to analyze students’ academic data. However, a significant [...] Read more.

With the advent of the big data era, it is vital to explore the information involved in this type of data. With the continuous development of higher education, the K-means clustering algorithm is widely used to analyze students’ academic data. However, a significant drawback of this method is that it is seriously affected by initial centroids of clustering and easily falls into local optima. Motivated by the fact that the chaos and swarm intelligence algorithm are frequently combined, we propose an approach for data clustering by Memristive Chaotic Sparrow Search Algorithm (MCSSA) in this paper. First, we introduce a memristive chaotic system, which has a property of conditional symmetry. We use the sequences generated by the memristive chaotic system to initialize the location of the sparrows. Then, MCSSA is applied before K-means for finding the optimal locations in the search space. Those locations are used as initial cluster centroids for the K-means algorithm to find final data clusters. Finally, the improved clustering algorithm is applied to the analysis of college students’ academic data, demonstrating the value and viability of the approach suggested in this paper. Through empirical research, it is also confirmed that this method can be promoted and applied. Full article

(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)

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14 pages, 277 KiB

Open AccessArticle

Mild Solutions for Fractional Impulsive Integro-Differential Evolution Equations with Nonlocal Conditions in Banach Spaces

by Ye Li and Biao Qu

Symmetry 2022, 14(8), 1655; https://doi.org/10.3390/sym14081655 - 10 Aug 2022

Cited by 4 | Viewed by 1769

Abstract

In this paper, by using the cosine family theory, measure of non-compactness, the Mönch fixed point theorem and the method of estimate step by step, we establish the existence theorems of mild solutions for fractional impulsive integro-differential evolution equations of order [...] Read more.

In this paper, by using the cosine family theory, measure of non-compactness, the Mönch fixed point theorem and the method of estimate step by step, we establish the existence theorems of mild solutions for fractional impulsive integro-differential evolution equations of order

1 < β \leq 2

with nonlocal conditions in Banach spaces under some weaker conditions. The results obtained herein generalizes and improves some known results. Finally, an example is presented for the demonstration of obtained results. Full article

(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)

20 pages, 2768 KiB

Open AccessArticle

Multi-Channel Data Aggregation Scheduling Based on the Chaotic Firework Algorithm for the Battery-Free Wireless Sensor Network

by Yao Lu, Xianming Wu, Liguo Yao, Taihua Zhang and Xiaosong Zhou

Symmetry 2022, 14(8), 1571; https://doi.org/10.3390/sym14081571 - 29 Jul 2022

Cited by 5 | Viewed by 1742

Abstract

The emergence of battery-free wireless sensor networks (benefiting from the ability to collect energy from the surroundings) has broken through the energy and lifetime limitations of traditional wireless sensor network systems, but also brings challenges to the sharing of network resources. In the [...] Read more.

The emergence of battery-free wireless sensor networks (benefiting from the ability to collect energy from the surroundings) has broken through the energy and lifetime limitations of traditional wireless sensor network systems, but also brings challenges to the sharing of network resources. In the multi-channel wireless communication environment, in particular, how to coordinate the communication time and occupied channels of a large number of sensor nodes from the perspective of optimizing the global network has become a research problem that must be solved. To reduce the transmission delay and the usage of wireless channels, a new multi-channel data aggregation scheduling method based on the chaotic firework algorithm is proposed in this paper. With the help of the generation function of feasible solutions, one scheduling set and a firework individual can be rapidly converted to each other. By the operations of firework explosions, the Gaussian mutation, and chaotic exploration, a sub-optimal scheduling set could be found during an acceptable time period. Finally, simulation results show that the new scheduling method has advantages in aggregation delay and occupied channels when compared with existing methods. Full article

(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)

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27 pages, 6261 KiB

Open AccessArticle

Symplectic Dynamics and Simultaneous Resonance Analysis of Memristor Circuit Based on Its van der Pol Oscillator

by Baonan Yang, Zhen Wang, Huaigu Tian and Jindong Liu

Symmetry 2022, 14(6), 1251; https://doi.org/10.3390/sym14061251 - 16 Jun 2022

Cited by 6 | Viewed by 2582

Abstract

A non-autonomous memristor circuit based on van der Pol oscillator with double periodically forcing term is presented and discussed. Firstly, the differences of the van der Pol oscillation of memristor model between Euler method and symplectic Euler method, four-order Runge–Kutta method (RK4) and [...] Read more.

A non-autonomous memristor circuit based on van der Pol oscillator with double periodically forcing term is presented and discussed. Firstly, the differences of the van der Pol oscillation of memristor model between Euler method and symplectic Euler method, four-order Runge–Kutta method (RK4) and four-order symplectic Runge–Kutta–Nyström method (SRKN4), symplectic Euler method and RK4 method, and symplectic Euler method and SRKN4 method in preserving structure are compared from theoretical and numerical simulations, the symmetry and structure preserving and numerical stability of symplectic scheme are demonstrated. Moreover, the analytic solution of the primary and subharmonic simultaneous resonance of this system is obtained by using the multi-scale method. Finally, based on the resonance relation of the system, the chaotic dynamics behaviors with different parameters are studied. Full article

(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)

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20 pages, 29741 KiB

Open AccessEditor’s ChoiceArticle

Design of a New Dimension-Changeable Hyperchaotic Model Based on Discrete Memristor

by Chengjing Wei, Guodong Li and Xiangliang Xu

Symmetry 2022, 14(5), 1019; https://doi.org/10.3390/sym14051019 - 17 May 2022

Cited by 16 | Viewed by 2575

Abstract

The application of a memristor in chaotic circuits is increasingly becoming a popular research topic. The influence of a memristor on the dynamics of chaotic systems is worthy of further exploration. In this paper, a multi-dimensional closed-loop coupling model based on a Logistic [...] Read more.

The application of a memristor in chaotic circuits is increasingly becoming a popular research topic. The influence of a memristor on the dynamics of chaotic systems is worthy of further exploration. In this paper, a multi-dimensional closed-loop coupling model based on a Logistic map and Sine map (CLS) is proposed. The new chaotic model is constructed by cascade operation in which the output of the Logistic map is used as the input of the Sine map. Additionally, the one-dimensional map is extended to any dimension through the coupling modulation. In order to further increase the complexity and stability of CLS, the discrete memristor model is introduced to construct a discrete memristor-based coupling model with a Logistic map and a Sine map (MCLS). By analyzing the Lyapunov exponents, bifurcation diagram, complexity, and the 0–1 test result, the comparison result between CLS and MCLS is obtained. The dynamics performance analysis shows that the Lyapunov exponents and bifurcation diagrams present symmetrical distribution with variations of some parameters. The MCLS has parameters whose values can be set in a wider range and can generate more complex and more stable chaotic sequences. It proves that the proposed discrete memristor-based closed-loop coupling model can produce any higher dimension hyperchaotic system and the discrete memristor model can effectively improve the performance of discrete chaotic map and make this hyperchaotic system more stable. Full article

(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)

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15 pages, 2266 KiB

Open AccessEditor’s ChoiceArticle

From Memristor-Modeled Jerk System to the Nonlinear Systems with Memristor

by Xianming Wu, Shaobo He, Weijie Tan and Huihai Wang

Symmetry 2022, 14(4), 659; https://doi.org/10.3390/sym14040659 - 24 Mar 2022

Cited by 9 | Viewed by 2985

Abstract

Based on the proposed generalized memristor, a new jerk system is proposed. The complex dynamics of the system are investigated by means of bifurcation diagrams, Lyapunov exponents, and MSampEn, and rich dynamics are observed. Moreover, the circuits of the generalized memristor and the [...] Read more.

Based on the proposed generalized memristor, a new jerk system is proposed. The complex dynamics of the system are investigated by means of bifurcation diagrams, Lyapunov exponents, and MSampEn, and rich dynamics are observed. Moreover, the circuits of the generalized memristor and the jerk system are physically implemented in the hardware level. The experimental results show that the memristor circuit can generate “8”-shaped pinched hysteresis loops, and the observed attractors match well with the numerical simulations results. In this paper, we summarize nonlinear systems with memristors in the references. It indicates that there are two symmetry methods to find a memristor model in nonlinear systems. However, some of them cannot be realized using the memristor devices, although a memristor model can be found. For example, the famous Lorenz system contains a memristor function, but it cannot be realized using the memristor device. The principles regarding whether nonlinear systems with a memristor function can be realized using a memristor device are discussed. Full article

(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)

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18 pages, 8423 KiB

Open AccessArticle

Symmetric Image Encryption Algorithm Based on a New Product Trigonometric Chaotic Map

by Qing Lu, Linlan Yu and Congxu Zhu

Symmetry 2022, 14(2), 373; https://doi.org/10.3390/sym14020373 - 13 Feb 2022

Cited by 29 | Viewed by 2748

Abstract

In the present work, a neotype chaotic product trigonometric map (PTM) system is proposed. We demonstrate the chaotic characteristics of a PTM system by using a series of complexity criteria, such as bifurcation diagrams, Lyapunov exponents, approximate entropy, permutation entropy, time-series diagrams, cobweb [...] Read more.

In the present work, a neotype chaotic product trigonometric map (PTM) system is proposed. We demonstrate the chaotic characteristics of a PTM system by using a series of complexity criteria, such as bifurcation diagrams, Lyapunov exponents, approximate entropy, permutation entropy, time-series diagrams, cobweb graphs, and NIST tests. It is proved that the PTM system has a wider chaotic parameter interval and more complex chaotic performance than the existing sine map system. In addition, a novel PTM based symmetric image encryption scheme is proposed, in which the key is related to the hash value of the image. The algorithm realizes the encryption strategy of one-graph-one-key, which can resist plaintext attack. A two-dimensional coordinate traversal matrix for image scrambling and a one-dimensional integer traversal sequence for image pixel value transformation encryption are generated by the pseudo-random integer generator (PRING). Security analysis and various simulation test results show that the proposed image encryption scheme has good cryptographic performance and high time efficiency. Full article

(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)

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19 pages, 83053 KiB

Open AccessArticle

Audio Encryption Algorithm Based on Chen Memristor Chaotic System

by Wanying Dai, Xiangliang Xu, Xiaoming Song and Guodong Li

Symmetry 2022, 14(1), 17; https://doi.org/10.3390/sym14010017 - 23 Dec 2021

Cited by 56 | Viewed by 6762

Abstract

The data space for audio signals is large, the correlation is strong, and the traditional encryption algorithm cannot meet the needs of efficiency and safety. To solve this problem, an audio encryption algorithm based on Chen memristor chaotic system is proposed. The core [...] Read more.

The data space for audio signals is large, the correlation is strong, and the traditional encryption algorithm cannot meet the needs of efficiency and safety. To solve this problem, an audio encryption algorithm based on Chen memristor chaotic system is proposed. The core idea of the algorithm is to encrypt the audio signal into the color image information. Most of the traditional audio encryption algorithms are transmitted in the form of noise, which makes it easy to attract the attention of attackers. In this paper, a special encryption method is used to obtain higher security. Firstly, the Fast Walsh–Hadamar Transform (FWHT) is used to compress and denoise the signal. Different from the Fast Fourier Transform (FFT) and the Discrete Cosine Transform (DCT), FWHT has good energy compression characteristics. In addition, compared with that of the triangular basis function of the Fast Fourier Transform, the rectangular basis function of the FWHT can be more effectively implemented in the digital circuit to transform the reconstructed dual-channel audio signal into the R and B layers of the digital image matrix, respectively. Furthermore, a new Chen memristor chaotic system solves the periodic window problems, such as the limited chaos range and nonuniform distribution. It can generate a mask block with high complexity and fill it into the G layer of the color image matrix to obtain a color audio image. In the next place, combining plaintext information with color audio images, interactive channel shuffling can not only weaken the correlation between adjacent samples, but also effectively resist selective plaintext attacks. Finally, the cryptographic block is used for overlapping diffusion encryption to fill the silence period of the speech signal, so as to obtain the ciphertext audio. Experimental results and comparative analysis show that the algorithm is suitable for different types of audio signals, and can resist many common cryptographic analysis attacks. Compared with that of similar audio encryption algorithms, the security index of the algorithm is better, and the efficiency of the algorithm is greatly improved. Full article

(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)

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